5.5 The Substitution Rule/15

${\begin{aligned}\ \int sin(\pi t)dt\end{aligned}}$

${\begin{aligned}let\;u&=\pi t\\[2ex]du&=\pi dx\\[2ex]{\frac {1}{\pi }}du&=dx\end{aligned}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \ \int sin(\pi t) dt = \int sin(u)(\frac{1}{\pi}du)= \int \frac{1}{\pi} (-cosu) + c = \int - \frac{1}{\pi} cos (\pi t) + c <span style="color: red \end{align} }